Yes, you are breaking the law. This is a contravention of the Companies Acts.
The limited company is a separate legal entity, and is therefore unaffected by your personal privacy concerns.
Do you have an accountant? They are usually willing to allow their office to be listed as the registered office address of their clients' companies.
Changing the registered office address would not, however, remove the requirement for you to list your personal address if you are a director and/or member of the company (unless you are the subject of a Confidentiality Order).
This will change next year when new provisions of the Companies Act 2006 kick in. Directors will then be able to specify a service address for inclusion on the public register. Their home address will still, however, need to be provided to Companies House, and can be disclosed in certain circumstances, such as to credit reference agencies.